Answer to Question #134611 in Physics for Naee

Question

One of the fastest recorded pitches in major-league baseball, thrown by Billy Wagner in 2003, was clocked at 101.0 mi/h. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away?

Answer 1

First, convert the values to conventional units:

101.0 mi/h is 45.15 m/s (divide by 2.237).

60.5 feet is 18.44 m (1 feet is 0.3048 m).

Calculate the time the ball moved horizontally assuming zero air friction:

$$t=\frac{d}{v}=\frac{18.44}{45.15}=0.408\text{ s}.$$

And this is the time the ball was falling vertically (see the diagram below). Thus, we can find the height of the pitch:

$$h=\frac{gt^2}{2}=0.816\text{ m}.$$